As of right now, Lightening Network suffers from the same flaw that allows mempool spamming in the Bitcoin network (making tons of incredibly small transactions with normal fees), and therefor if there are a large number of microtransactions, will suffer from the same flaw.
All channel updates are broadcast to everyone. How badly that will suck depends on how fast updates happen, but it's likely to get painful somewhere between 10,000 and 1,000,000 channels.
It is important to note that the mempool attack works by creating an artificial demand for space in a networks mempool. The transaction fee is average or above average, but there is little to no output. This attack works because it forces real transactions to pay higher fees.
However in LN the problem is different. It is more a question of what the network bandwidth can handle. This is not to say the issue is not fixable, the LN Developer listed in the source goes on to say that this system is not optimized. A possible solution would be for the seller to only send the preimage (for more information on how LN transactions hop through the network) to the those who have created an HTLC with the seller and to pass the preimage along the chain of debt until it reaches the payee.
Source: RustyReddit, RustyReddit